This paper presents an overlapping decomposition method to approximate the throughput of production systems with rework loops. The idea is to decompose the system into overlapped serial production lines, with the overlapping machines modified to accommodate the interactions with machines and buffers in other lines. The convergence of the iterative procedure and the uniqueness of the solution are proved analytically. The accuracy of the estimate is justified numerically and illustrated by a case study at an automotive assembly plant.
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Jingshan Li (2004) studied this question.
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